Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4584070 | Journal of Algebra | 2015 | 31 Pages |
Let Γ be a generic subgroup of the multiplicative group C⁎C⁎ of nonzero complex numbers. We define a class of Lie algebras associated to Γ, called twisted Γ-Lie algebras, which are natural generalizations of the twisted affine Lie algebras. Starting from an arbitrary even sublattice Q of ZNZN and an arbitrary finite order isometry of ZNZN preserving Q, we construct a family of twisted Γ-vertex operators acting on generalized Fock spaces which afford irreducible representations for certain twisted Γ-Lie algebras. As an application, this recovers a number of known vertex operator realizations for infinite dimensional Lie algebras, such as twisted affine Lie algebras, extended affine Lie algebras of type A, trigonometric Lie algebras of series A and B, unitary Lie algebras, and BC-graded Lie algebras.